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Shared Qs (013)


  1. Question

    Here are some common (and less common) parent functions:

    name \(f(x)=\)
    constant 1
    linear \(x\)
    absolute \(|x|\)
    quadratic \(x^2\)
    cubic \(x^3\)
    reciprocal \(\frac{1}{x}\)
    square root \(\sqrt{x}\)
    cube root \(\sqrt[3]{x}\)
    sine \(\sin(x)\)
    cosine \(\cos(x)\)
    tangent \(\tan(x)\)
    ceiling \(\lceil x \rceil\)
    floor \(\lfloor x \rfloor\)
    exponential \(e^x\)
    logarithmic \(\ln(x)\)
    logistic \(\frac{e^x}{e^x+1}\)
    squared reciprocal \(\frac{1}{x^2}\)

    Match the graphs with their names.

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    Solution


  2. Question

    Here are some common (and less common) parent functions:

    name \(f(x)=\)
    constant 1
    linear \(x\)
    absolute \(|x|\)
    quadratic \(x^2\)
    cubic \(x^3\)
    reciprocal \(\frac{1}{x}\)
    square root \(\sqrt{x}\)
    cube root \(\sqrt[3]{x}\)
    sine \(\sin(x)\)
    cosine \(\cos(x)\)
    tangent \(\tan(x)\)
    ceiling \(\lceil x \rceil\)
    floor \(\lfloor x \rfloor\)
    exponential \(e^x\)
    logarithmic \(\ln(x)\)
    logistic \(\frac{e^x}{e^x+1}\)
    squared reciprocal \(\frac{1}{x^2}\)

    Match the graphs with their names.

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    Solution


  3. Question

    Here are some common (and less common) parent functions:

    name \(f(x)=\)
    constant 1
    linear \(x\)
    absolute \(|x|\)
    quadratic \(x^2\)
    cubic \(x^3\)
    reciprocal \(\frac{1}{x}\)
    square root \(\sqrt{x}\)
    cube root \(\sqrt[3]{x}\)
    sine \(\sin(x)\)
    cosine \(\cos(x)\)
    tangent \(\tan(x)\)
    ceiling \(\lceil x \rceil\)
    floor \(\lfloor x \rfloor\)
    exponential \(e^x\)
    logarithmic \(\ln(x)\)
    logistic \(\frac{e^x}{e^x+1}\)
    squared reciprocal \(\frac{1}{x^2}\)

    Match the graphs with their names.

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    Solution


  4. Question

    Here are some common (and less common) parent functions:

    name \(f(x)=\)
    constant 1
    linear \(x\)
    absolute \(|x|\)
    quadratic \(x^2\)
    cubic \(x^3\)
    reciprocal \(\frac{1}{x}\)
    square root \(\sqrt{x}\)
    cube root \(\sqrt[3]{x}\)
    sine \(\sin(x)\)
    cosine \(\cos(x)\)
    tangent \(\tan(x)\)
    ceiling \(\lceil x \rceil\)
    floor \(\lfloor x \rfloor\)
    exponential \(e^x\)
    logarithmic \(\ln(x)\)
    logistic \(\frac{e^x}{e^x+1}\)
    squared reciprocal \(\frac{1}{x^2}\)

    Match the graphs with their names.

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    Solution


  5. Question

    Here are some common (and less common) parent functions:

    name \(f(x)=\)
    constant 1
    linear \(x\)
    absolute \(|x|\)
    quadratic \(x^2\)
    cubic \(x^3\)
    reciprocal \(\frac{1}{x}\)
    square root \(\sqrt{x}\)
    cube root \(\sqrt[3]{x}\)
    sine \(\sin(x)\)
    cosine \(\cos(x)\)
    tangent \(\tan(x)\)
    ceiling \(\lceil x \rceil\)
    floor \(\lfloor x \rfloor\)
    exponential \(e^x\)
    logarithmic \(\ln(x)\)
    logistic \(\frac{e^x}{e^x+1}\)
    squared reciprocal \(\frac{1}{x^2}\)

    Match the graphs with their names.

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    Solution


  6. Question

    Here are some common (and less common) parent functions:

    name \(f(x)=\)
    constant 1
    linear \(x\)
    absolute \(|x|\)
    quadratic \(x^2\)
    cubic \(x^3\)
    reciprocal \(\frac{1}{x}\)
    square root \(\sqrt{x}\)
    cube root \(\sqrt[3]{x}\)
    sine \(\sin(x)\)
    cosine \(\cos(x)\)
    tangent \(\tan(x)\)
    ceiling \(\lceil x \rceil\)
    floor \(\lfloor x \rfloor\)
    exponential \(e^x\)
    logarithmic \(\ln(x)\)
    logistic \(\frac{e^x}{e^x+1}\)
    squared reciprocal \(\frac{1}{x^2}\)

    Match the graphs with their names.

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    Solution


  7. Question

    Here are some common (and less common) parent functions:

    name \(f(x)=\)
    constant 1
    linear \(x\)
    absolute \(|x|\)
    quadratic \(x^2\)
    cubic \(x^3\)
    reciprocal \(\frac{1}{x}\)
    square root \(\sqrt{x}\)
    cube root \(\sqrt[3]{x}\)
    sine \(\sin(x)\)
    cosine \(\cos(x)\)
    tangent \(\tan(x)\)
    ceiling \(\lceil x \rceil\)
    floor \(\lfloor x \rfloor\)
    exponential \(e^x\)
    logarithmic \(\ln(x)\)
    logistic \(\frac{e^x}{e^x+1}\)
    squared reciprocal \(\frac{1}{x^2}\)

    Match the graphs with their names.

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    Solution


  8. Question

    Here are some common (and less common) parent functions:

    name \(f(x)=\)
    constant 1
    linear \(x\)
    absolute \(|x|\)
    quadratic \(x^2\)
    cubic \(x^3\)
    reciprocal \(\frac{1}{x}\)
    square root \(\sqrt{x}\)
    cube root \(\sqrt[3]{x}\)
    sine \(\sin(x)\)
    cosine \(\cos(x)\)
    tangent \(\tan(x)\)
    ceiling \(\lceil x \rceil\)
    floor \(\lfloor x \rfloor\)
    exponential \(e^x\)
    logarithmic \(\ln(x)\)
    logistic \(\frac{e^x}{e^x+1}\)
    squared reciprocal \(\frac{1}{x^2}\)

    Match the graphs with their names.

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    Solution


  9. Question

    Here are some common (and less common) parent functions:

    name \(f(x)=\)
    constant 1
    linear \(x\)
    absolute \(|x|\)
    quadratic \(x^2\)
    cubic \(x^3\)
    reciprocal \(\frac{1}{x}\)
    square root \(\sqrt{x}\)
    cube root \(\sqrt[3]{x}\)
    sine \(\sin(x)\)
    cosine \(\cos(x)\)
    tangent \(\tan(x)\)
    ceiling \(\lceil x \rceil\)
    floor \(\lfloor x \rfloor\)
    exponential \(e^x\)
    logarithmic \(\ln(x)\)
    logistic \(\frac{e^x}{e^x+1}\)
    squared reciprocal \(\frac{1}{x^2}\)

    Match the graphs with their names.

    plot of chunk unnamed-chunk-1

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    Solution


  10. Question

    Here are some common (and less common) parent functions:

    name \(f(x)=\)
    constant 1
    linear \(x\)
    absolute \(|x|\)
    quadratic \(x^2\)
    cubic \(x^3\)
    reciprocal \(\frac{1}{x}\)
    square root \(\sqrt{x}\)
    cube root \(\sqrt[3]{x}\)
    sine \(\sin(x)\)
    cosine \(\cos(x)\)
    tangent \(\tan(x)\)
    ceiling \(\lceil x \rceil\)
    floor \(\lfloor x \rfloor\)
    exponential \(e^x\)
    logarithmic \(\ln(x)\)
    logistic \(\frac{e^x}{e^x+1}\)
    squared reciprocal \(\frac{1}{x^2}\)

    Match the graphs with their names.

    plot of chunk unnamed-chunk-1

    plot of chunk unnamed-chunk-1

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    Solution


  11. Question

    Consider the quadratic function graphed below:

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    Solution


  12. Question

    Consider the quadratic function graphed below:

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    Solution


  13. Question

    Consider the quadratic function graphed below:

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    Solution


  14. Question

    Consider the quadratic function graphed below:

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    Solution


  15. Question

    Consider the quadratic function graphed below:

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    Solution


  16. Question

    Consider the quadratic function graphed below:

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    Solution


  17. Question

    Consider the quadratic function graphed below:

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    Solution


  18. Question

    Consider the quadratic function graphed below:

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    Solution


  19. Question

    Consider the quadratic function graphed below:

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    Solution


  20. Question

    Consider the quadratic function graphed below:

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    Solution


  21. Question

    Which plot matches the function:

    \[f(x) = \left|{x - 1}\right| + 6\]

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    1. Plot 1
    2. Plot 2
    3. Plot 3
    4. Plot 4

    Solution


  22. Question

    Which plot matches the function:

    \[f(x) = \left|{x + 4}\right| - 6\]

    plot of chunk unnamed-chunk-2


    1. Plot 1
    2. Plot 2
    3. Plot 3
    4. Plot 4

    Solution


  23. Question

    Which plot matches the function:

    \[f(x) = \left|{x + 2}\right| + 1\]

    plot of chunk unnamed-chunk-2


    1. Plot 1
    2. Plot 2
    3. Plot 3
    4. Plot 4

    Solution


  24. Question

    Which plot matches the function:

    \[f(x) = - \left|{x - 3}\right| - 6\]

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    1. Plot 1
    2. Plot 2
    3. Plot 3
    4. Plot 4

    Solution


  25. Question

    Which plot matches the function:

    \[f(x) = 4 - \left|{x + 5}\right|\]

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    1. Plot 1
    2. Plot 2
    3. Plot 3
    4. Plot 4

    Solution


  26. Question

    Which plot matches the function:

    \[f(x) = \left|{x + 4}\right| + 5\]

    plot of chunk unnamed-chunk-2


    1. Plot 1
    2. Plot 2
    3. Plot 3
    4. Plot 4

    Solution


  27. Question

    Which plot matches the function:

    \[f(x) = \left|{x - 3}\right| - 4\]

    plot of chunk unnamed-chunk-2


    1. Plot 1
    2. Plot 2
    3. Plot 3
    4. Plot 4

    Solution


  28. Question

    Which plot matches the function:

    \[f(x) = - \left|{x + 6}\right| - 4\]

    plot of chunk unnamed-chunk-2


    1. Plot 1
    2. Plot 2
    3. Plot 3
    4. Plot 4

    Solution


  29. Question

    Which plot matches the function:

    \[f(x) = 5 - \left|{x - 2}\right|\]

    plot of chunk unnamed-chunk-2


    1. Plot 1
    2. Plot 2
    3. Plot 3
    4. Plot 4

    Solution


  30. Question

    Which plot matches the function:

    \[f(x) = \left|{x - 3}\right| + 1\]

    plot of chunk unnamed-chunk-2


    1. Plot 1
    2. Plot 2
    3. Plot 3
    4. Plot 4

    Solution


  31. Question

    Let functions \(f\) and \(g\) be defined by the table below.

    \(x\) \(f(x)\) \(g(x)\)
    1 9 1
    2 3 2
    3 7 3
    4 6 6
    5 10 10
    6 5 9
    7 4 7
    8 2 4
    9 8 5
    10 1 8

    Evaluate the following:



    Solution


  32. Question

    Let functions \(f\) and \(g\) be defined by the table below.

    \(x\) \(f(x)\) \(g(x)\)
    1 9 9
    2 7 7
    3 1 3
    4 6 1
    5 4 2
    6 3 10
    7 10 4
    8 5 8
    9 2 6
    10 8 5

    Evaluate the following:



    Solution


  33. Question

    Let functions \(f\) and \(g\) be defined by the table below.

    \(x\) \(f(x)\) \(g(x)\)
    1 1 5
    2 6 4
    3 10 2
    4 3 7
    5 8 9
    6 4 1
    7 7 10
    8 5 6
    9 9 3
    10 2 8

    Evaluate the following:



    Solution


  34. Question

    Let functions \(f\) and \(g\) be defined by the table below.

    \(x\) \(f(x)\) \(g(x)\)
    1 4 10
    2 5 7
    3 9 3
    4 6 9
    5 8 6
    6 10 1
    7 3 8
    8 1 2
    9 2 4
    10 7 5

    Evaluate the following:



    Solution


  35. Question

    Let functions \(f\) and \(g\) be defined by the table below.

    \(x\) \(f(x)\) \(g(x)\)
    1 10 1
    2 6 8
    3 1 4
    4 3 6
    5 5 2
    6 2 9
    7 9 3
    8 4 10
    9 8 5
    10 7 7

    Evaluate the following:



    Solution


  36. Question

    Let functions \(f\) and \(g\) be defined by the table below.

    \(x\) \(f(x)\) \(g(x)\)
    1 3 8
    2 5 10
    3 2 6
    4 7 3
    5 10 5
    6 9 7
    7 1 2
    8 8 9
    9 4 4
    10 6 1

    Evaluate the following:



    Solution


  37. Question

    Let functions \(f\) and \(g\) be defined by the table below.

    \(x\) \(f(x)\) \(g(x)\)
    1 1 5
    2 5 1
    3 6 3
    4 8 10
    5 2 6
    6 7 2
    7 10 7
    8 4 9
    9 9 4
    10 3 8

    Evaluate the following:



    Solution


  38. Question

    Let functions \(f\) and \(g\) be defined by the table below.

    \(x\) \(f(x)\) \(g(x)\)
    1 6 7
    2 10 1
    3 8 6
    4 2 10
    5 5 4
    6 1 8
    7 7 3
    8 3 5
    9 4 2
    10 9 9

    Evaluate the following:



    Solution


  39. Question

    Let functions \(f\) and \(g\) be defined by the table below.

    \(x\) \(f(x)\) \(g(x)\)
    1 3 8
    2 9 4
    3 8 2
    4 10 7
    5 5 1
    6 2 10
    7 7 3
    8 1 9
    9 4 5
    10 6 6

    Evaluate the following:



    Solution


  40. Question

    Let functions \(f\) and \(g\) be defined by the table below.

    \(x\) \(f(x)\) \(g(x)\)
    1 8 5
    2 1 10
    3 5 8
    4 7 2
    5 3 1
    6 6 4
    7 9 7
    8 10 3
    9 4 9
    10 2 6

    Evaluate the following:



    Solution


  41. Question

    Let functions \(f\) and \(g\) be defined by the graph below.

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    Evaluate the following:



    Solution


  42. Question

    Let functions \(f\) and \(g\) be defined by the graph below.

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    Evaluate the following:



    Solution


  43. Question

    Let functions \(f\) and \(g\) be defined by the graph below.

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    Evaluate the following:



    Solution


  44. Question

    Let functions \(f\) and \(g\) be defined by the graph below.

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    Evaluate the following:



    Solution


  45. Question

    Let functions \(f\) and \(g\) be defined by the graph below.

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    Evaluate the following:



    Solution


  46. Question

    Let functions \(f\) and \(g\) be defined by the graph below.

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    Evaluate the following:



    Solution


  47. Question

    Let functions \(f\) and \(g\) be defined by the graph below.

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    Evaluate the following:



    Solution


  48. Question

    Let functions \(f\) and \(g\) be defined by the graph below.

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    Evaluate the following:



    Solution


  49. Question

    Let functions \(f\) and \(g\) be defined by the graph below.

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    Evaluate the following:



    Solution


  50. Question

    Let functions \(f\) and \(g\) be defined by the graph below.

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    Evaluate the following:



    Solution


  51. Question

    Let function \(f\) be defined by the graph below.

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    Solution


  52. Question

    Let function \(f\) be defined by the graph below.

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    Solution


  53. Question

    Let function \(f\) be defined by the graph below.

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    Solution


  54. Question

    Let function \(f\) be defined by the graph below.

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    Solution


  55. Question

    Let function \(f\) be defined by the graph below.

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    Solution


  56. Question

    Let function \(f\) be defined by the graph below.

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    Solution


  57. Question

    Let function \(f\) be defined by the graph below.

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    Solution


  58. Question

    Let function \(f\) be defined by the graph below.

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    Solution


  59. Question

    Let function \(f\) be defined by the graph below.

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    Solution


  60. Question

    Let function \(f\) be defined by the graph below.

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    Solution


  61. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    2 8
    3 3
    6 4
    7 2

    Let \(g(x)\) be defined with the equation \(g(x)=f(x+4)-3\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  62. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    2 5
    4 6
    6 4
    8 3

    Let \(g(x)\) be defined with the equation \(g(x)=f(x+4)+5\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  63. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    2 6
    4 2
    7 7
    8 5

    Let \(g(x)\) be defined with the equation \(g(x)=f(x-3)+4\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  64. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    2 8
    4 7
    5 3
    6 2

    Let \(g(x)\) be defined with the equation \(g(x)=f(x-5)-2\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  65. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    5 6
    6 8
    7 3
    8 4

    Let \(g(x)\) be defined with the equation \(g(x)=f(x+1)-3\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  66. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    3 4
    5 7
    6 8
    7 2

    Let \(g(x)\) be defined with the equation \(g(x)=f(x+5)-3\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  67. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    2 5
    5 2
    6 4
    8 8

    Let \(g(x)\) be defined with the equation \(g(x)=f(x+5)-2\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  68. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    4 6
    5 2
    6 8
    7 7

    Let \(g(x)\) be defined with the equation \(g(x)=f(x-3)+1\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  69. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    2 4
    5 7
    6 5
    8 6

    Let \(g(x)\) be defined with the equation \(g(x)=f(x-5)-3\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  70. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    3 5
    4 2
    6 3
    8 8

    Let \(g(x)\) be defined with the equation \(g(x)=f(x+5)-4\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  71. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    6 54
    12 48
    18 30
    24 42

    Let \(g(x)\) be defined with the equation \(g(x)=2\, f(\frac{1}{3}x)\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  72. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    6 54
    12 60
    18 36
    24 42

    Let \(g(x)\) be defined with the equation \(g(x)=\frac{1}{2}\,f(3x)\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  73. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    6 54
    12 42
    18 60
    24 30

    Let \(g(x)\) be defined with the equation \(g(x)=3\, f(\frac{1}{2}x)\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  74. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    6 42
    12 54
    18 30
    24 36

    Let \(g(x)\) be defined with the equation \(g(x)=2\, f(\frac{1}{3}x)\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  75. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    6 42
    12 30
    18 60
    24 54

    Let \(g(x)\) be defined with the equation \(g(x)=\frac{1}{2}\,f(3x)\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  76. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    6 60
    12 30
    18 54
    24 48

    Let \(g(x)\) be defined with the equation \(g(x)=\frac{1}{2}\,f(3x)\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  77. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    6 48
    12 54
    18 60
    24 42

    Let \(g(x)\) be defined with the equation \(g(x)=2\, f(\frac{1}{3}x)\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  78. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    6 30
    12 36
    18 42
    24 48

    Let \(g(x)\) be defined with the equation \(g(x)=\frac{1}{3}\,f(2x)\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  79. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    6 48
    12 60
    18 30
    24 54

    Let \(g(x)\) be defined with the equation \(g(x)=3\, f(\frac{1}{2}x)\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  80. Question

    Let \(f(x)\) be defined by the table below:

    \(x\) \(f(x)\)
    6 36
    12 42
    18 30
    24 54

    Let \(g(x)\) be defined with the equation \(g(x)=\frac{1}{2}\,f(3x)\). What are the 4 corresponding points on \(g\)? (Use same order.)

    \(x\) \(g(x)\)


    Solution


  81. Question

    A simple piece-wise function \(f\) is plotted below.

    plot of chunk unnamed-chunk-1

    It’s general daughter function, having translations, reflections, and stretches, can be expressed with 4 parameters: \(a\), \(b\), \(h\), and \(k\).

    \[g(x) = a\, f(b(x-h))+k \]

    Compared to the parent function, the daughter is stretched vertically by a factor of \(a\), stretch horizontally by a factor of \(\frac{1}{b}\), and then shifted right \(h\) and up \(k\).

    Notice, a left or down shift gives a negative value for \(h\) or \(k\). Also, a negative stretch factor causes a reflection.

    Each of those four parameters is randomly assigned \(\pm 2\) or \(\pm \frac{1}{2}\). Determine the four parameters of the daughter by inspecting the daughter’s graph:

    plot of chunk unnamed-chunk-2

    Also, write the equation to define the daughter.

    \(g(x) =\) \(f(\) \((x\) \()\)



    Solution


  82. Question

    A simple piece-wise function \(f\) is plotted below.

    plot of chunk unnamed-chunk-1

    It’s general daughter function, having translations, reflections, and stretches, can be expressed with 4 parameters: \(a\), \(b\), \(h\), and \(k\).

    \[g(x) = a\, f(b(x-h))+k \]

    Compared to the parent function, the daughter is stretched vertically by a factor of \(a\), stretch horizontally by a factor of \(\frac{1}{b}\), and then shifted right \(h\) and up \(k\).

    Notice, a left or down shift gives a negative value for \(h\) or \(k\). Also, a negative stretch factor causes a reflection.

    Each of those four parameters is randomly assigned \(\pm 2\) or \(\pm \frac{1}{2}\). Determine the four parameters of the daughter by inspecting the daughter’s graph:

    plot of chunk unnamed-chunk-2

    Also, write the equation to define the daughter.

    \(g(x) =\) \(f(\) \((x\) \()\)



    Solution


  83. Question

    A simple piece-wise function \(f\) is plotted below.

    plot of chunk unnamed-chunk-1

    It’s general daughter function, having translations, reflections, and stretches, can be expressed with 4 parameters: \(a\), \(b\), \(h\), and \(k\).

    \[g(x) = a\, f(b(x-h))+k \]

    Compared to the parent function, the daughter is stretched vertically by a factor of \(a\), stretch horizontally by a factor of \(\frac{1}{b}\), and then shifted right \(h\) and up \(k\).

    Notice, a left or down shift gives a negative value for \(h\) or \(k\). Also, a negative stretch factor causes a reflection.

    Each of those four parameters is randomly assigned \(\pm 2\) or \(\pm \frac{1}{2}\). Determine the four parameters of the daughter by inspecting the daughter’s graph:

    plot of chunk unnamed-chunk-2

    Also, write the equation to define the daughter.

    \(g(x) =\) \(f(\) \((x\) \()\)



    Solution


  84. Question

    A simple piece-wise function \(f\) is plotted below.

    plot of chunk unnamed-chunk-1

    It’s general daughter function, having translations, reflections, and stretches, can be expressed with 4 parameters: \(a\), \(b\), \(h\), and \(k\).

    \[g(x) = a\, f(b(x-h))+k \]

    Compared to the parent function, the daughter is stretched vertically by a factor of \(a\), stretch horizontally by a factor of \(\frac{1}{b}\), and then shifted right \(h\) and up \(k\).

    Notice, a left or down shift gives a negative value for \(h\) or \(k\). Also, a negative stretch factor causes a reflection.

    Each of those four parameters is randomly assigned \(\pm 2\) or \(\pm \frac{1}{2}\). Determine the four parameters of the daughter by inspecting the daughter’s graph:

    plot of chunk unnamed-chunk-2

    Also, write the equation to define the daughter.

    \(g(x) =\) \(f(\) \((x\) \()\)



    Solution


  85. Question

    A simple piece-wise function \(f\) is plotted below.

    plot of chunk unnamed-chunk-1

    It’s general daughter function, having translations, reflections, and stretches, can be expressed with 4 parameters: \(a\), \(b\), \(h\), and \(k\).

    \[g(x) = a\, f(b(x-h))+k \]

    Compared to the parent function, the daughter is stretched vertically by a factor of \(a\), stretch horizontally by a factor of \(\frac{1}{b}\), and then shifted right \(h\) and up \(k\).

    Notice, a left or down shift gives a negative value for \(h\) or \(k\). Also, a negative stretch factor causes a reflection.

    Each of those four parameters is randomly assigned \(\pm 2\) or \(\pm \frac{1}{2}\). Determine the four parameters of the daughter by inspecting the daughter’s graph:

    plot of chunk unnamed-chunk-2

    Also, write the equation to define the daughter.

    \(g(x) =\) \(f(\) \((x\) \()\)



    Solution


  86. Question

    A simple piece-wise function \(f\) is plotted below.

    plot of chunk unnamed-chunk-1

    It’s general daughter function, having translations, reflections, and stretches, can be expressed with 4 parameters: \(a\), \(b\), \(h\), and \(k\).

    \[g(x) = a\, f(b(x-h))+k \]

    Compared to the parent function, the daughter is stretched vertically by a factor of \(a\), stretch horizontally by a factor of \(\frac{1}{b}\), and then shifted right \(h\) and up \(k\).

    Notice, a left or down shift gives a negative value for \(h\) or \(k\). Also, a negative stretch factor causes a reflection.

    Each of those four parameters is randomly assigned \(\pm 2\) or \(\pm \frac{1}{2}\). Determine the four parameters of the daughter by inspecting the daughter’s graph:

    plot of chunk unnamed-chunk-2

    Also, write the equation to define the daughter.

    \(g(x) =\) \(f(\) \((x\) \()\)



    Solution


  87. Question

    A simple piece-wise function \(f\) is plotted below.

    plot of chunk unnamed-chunk-1

    It’s general daughter function, having translations, reflections, and stretches, can be expressed with 4 parameters: \(a\), \(b\), \(h\), and \(k\).

    \[g(x) = a\, f(b(x-h))+k \]

    Compared to the parent function, the daughter is stretched vertically by a factor of \(a\), stretch horizontally by a factor of \(\frac{1}{b}\), and then shifted right \(h\) and up \(k\).

    Notice, a left or down shift gives a negative value for \(h\) or \(k\). Also, a negative stretch factor causes a reflection.

    Each of those four parameters is randomly assigned \(\pm 2\) or \(\pm \frac{1}{2}\). Determine the four parameters of the daughter by inspecting the daughter’s graph:

    plot of chunk unnamed-chunk-2

    Also, write the equation to define the daughter.

    \(g(x) =\) \(f(\) \((x\) \()\)



    Solution


  88. Question

    A simple piece-wise function \(f\) is plotted below.

    plot of chunk unnamed-chunk-1

    It’s general daughter function, having translations, reflections, and stretches, can be expressed with 4 parameters: \(a\), \(b\), \(h\), and \(k\).

    \[g(x) = a\, f(b(x-h))+k \]

    Compared to the parent function, the daughter is stretched vertically by a factor of \(a\), stretch horizontally by a factor of \(\frac{1}{b}\), and then shifted right \(h\) and up \(k\).

    Notice, a left or down shift gives a negative value for \(h\) or \(k\). Also, a negative stretch factor causes a reflection.

    Each of those four parameters is randomly assigned \(\pm 2\) or \(\pm \frac{1}{2}\). Determine the four parameters of the daughter by inspecting the daughter’s graph:

    plot of chunk unnamed-chunk-2

    Also, write the equation to define the daughter.

    \(g(x) =\) \(f(\) \((x\) \()\)



    Solution


  89. Question

    A simple piece-wise function \(f\) is plotted below.

    plot of chunk unnamed-chunk-1

    It’s general daughter function, having translations, reflections, and stretches, can be expressed with 4 parameters: \(a\), \(b\), \(h\), and \(k\).

    \[g(x) = a\, f(b(x-h))+k \]

    Compared to the parent function, the daughter is stretched vertically by a factor of \(a\), stretch horizontally by a factor of \(\frac{1}{b}\), and then shifted right \(h\) and up \(k\).

    Notice, a left or down shift gives a negative value for \(h\) or \(k\). Also, a negative stretch factor causes a reflection.

    Each of those four parameters is randomly assigned \(\pm 2\) or \(\pm \frac{1}{2}\). Determine the four parameters of the daughter by inspecting the daughter’s graph:

    plot of chunk unnamed-chunk-2

    Also, write the equation to define the daughter.

    \(g(x) =\) \(f(\) \((x\) \()\)



    Solution


  90. Question

    A simple piece-wise function \(f\) is plotted below.

    plot of chunk unnamed-chunk-1

    It’s general daughter function, having translations, reflections, and stretches, can be expressed with 4 parameters: \(a\), \(b\), \(h\), and \(k\).

    \[g(x) = a\, f(b(x-h))+k \]

    Compared to the parent function, the daughter is stretched vertically by a factor of \(a\), stretch horizontally by a factor of \(\frac{1}{b}\), and then shifted right \(h\) and up \(k\).

    Notice, a left or down shift gives a negative value for \(h\) or \(k\). Also, a negative stretch factor causes a reflection.

    Each of those four parameters is randomly assigned \(\pm 2\) or \(\pm \frac{1}{2}\). Determine the four parameters of the daughter by inspecting the daughter’s graph:

    plot of chunk unnamed-chunk-2

    Also, write the equation to define the daughter.

    \(g(x) =\) \(f(\) \((x\) \()\)



    Solution